i have fun at both. i play lotsa online games but i love playing xbox live on my 360. i think it all depends on who you play with and what game you are playing. make it fun and either way is fine with me.
For me it depends on the game. I enjoy WoW which is a PC game, very fun. I also enjoy Halo which is only a Xbox game. My recomendation is to pick out what games you want to play and then you will know what you need to play them.
Online Console Gaming is good for those shorter games. I think I would get rather large blisters on my thumbs if I was putting in the few weeks that are required for an MMORPG on a console.